Advertisements
Advertisements
प्रश्न
The distance between points P(–1, 1) and Q(5, –7) is ______.
विकल्प
11 cm
10 cm
5 cm
7 cm
Advertisements
उत्तर
The distance between points P(–1, 1) and Q(5, –7) is 10 cm.
Explanation:
Let P(x1, y1) = P(–1, 1) and Q(x2, y2) = Q(5, –7)
Here, x1 = –1, y1 = 1, x2 = 5, y2 = –7
By distance formula,
`d(P, Q) = sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2)`
= `sqrt([5 - (-1)]^2 + (-7 - 1)^2)`
= `sqrt(36 + 64)`
= `sqrt(100)`
= 10 cm
APPEARS IN
संबंधित प्रश्न
If the point P(2, 2) is equidistant from the points A(−2, k) and B(−2k, −3), find k. Also find the length of AP.
If the distances of P(x, y) from A(5, 1) and B(–1, 5) are equal, then prove that 3x = 2y
Find the centre of the circle passing through (6, -6), (3, -7) and (3, 3)
Two opposite vertices of a square are (-1, 2) and (3, 2). Find the coordinates of other two
vertices.
Find the distance between the following pair of points.
R(0, -3), S(0, `5/2`)
Find the distance between the following pairs of point in the coordinate plane :
(13 , 7) and (4 , -5)
Find the distance of the following point from the origin :
(0 , 11)
Prove that the points (4 , 6) , (- 1 , 5) , (- 2, 0) and (3 , 1) are the vertices of a rhombus.
A point P lies on the x-axis and another point Q lies on the y-axis.
Write the abscissa of point Q.
Given A = (3, 1) and B = (0, y - 1). Find y if AB = 5.
If the length of the segment joining point L(x, 7) and point M(1, 15) is 10 cm, then the value of x is ______.
Find distance between point A(–3, 4) and origin O.
Find distance between points O(0, 0) and B(–5, 12).
Find distance CD where C(– 3a, a), D(a, – 2a)
Show that P(– 2, 2), Q(2, 2) and R(2, 7) are vertices of a right angled triangle
Show that the points (0, –1), (8, 3), (6, 7) and (– 2, 3) are vertices of a rectangle.
If the distance between the points (x, -1) and (3, 2) is 5, then the value of x is ______.
Case Study -2
A hockey field is the playing surface for the game of hockey. Historically, the game was played on natural turf (grass) but nowadays it is predominantly played on an artificial turf.
It is rectangular in shape - 100 yards by 60 yards. Goals consist of two upright posts placed equidistant from the centre of the backline, joined at the top by a horizontal crossbar. The inner edges of the posts must be 3.66 metres (4 yards) apart, and the lower edge of the crossbar must be 2.14 metres (7 feet) above the ground.
Each team plays with 11 players on the field during the game including the goalie. Positions you might play include -
- Forward: As shown by players A, B, C and D.
- Midfielders: As shown by players E, F and G.
- Fullbacks: As shown by players H, I and J.
- Goalie: As shown by player K.
Using the picture of a hockey field below, answer the questions that follow:
The point on x axis equidistant from I and E is ______.
A circle has its centre at the origin and a point P(5, 0) lies on it. The point Q(6, 8) lies outside the circle.
Show that Alia's house, Shagun's house and library for an isosceles right triangle.
